Discontinuity in cubic equations of state: Impact of attraction term mixing rule on combustion simulation

Abstract

High-pressure or cryogenic conditions relevant to hydrogen applications introduce non-idealities in the property of fluid, which requires using real gas equations of state in numerical simulation. However, intrinsic but non-physical discontinuities exist in the partial derivatives with respect to temperature of the molecular attraction term of popular cubic equations of state. This feature is related to the van der Waals mixing rule and results in non-physical discontinuities in the thermodynamic functions and simulation results. Thermodynamic properties of dry air were used to illustrate the impact of discontinuities on the thermodynamic functions whereas steady detonation simulation and constant volume reactor simulation were performed to discuss the impact of the discontinuities on combustion modeling. We show that the accuracy of the solution can be decreased by up to several percents. In addition, an increase of computation cost is induced in the vicinity of the discontinuities when adaptive time-stepping is adopted in the simulation. A correlation previously proposed in the literature to remove the discontinuity issue was tested and proved efficient to limit the decrease of the time-step.